t^4-11t^2+18=0

Solution for t^4-11t^2+18=0 equation:

Simplifying
t4 + -11t2 + 18 = 0

Reorder the terms:
18 + -11t2 + t4 = 0

Solving
18 + -11t2 + t4 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + -1t2)(9 + -1t2) = 0

Factor a difference between two squares.
(2 + -1t2)((3 + t)(3 + -1t)) = 0

Subproblem 1
Set the factor '(2 + -1t2)' equal to zero and attempt to solve:

Simplifying
2 + -1t2 = 0

Solving
2 + -1t2 = 0

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t2 = 0 + -2
-1t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1t2 = -2

Divide each side by '-1'.
t2 = 2

Simplifying
t2 = 2

Take the square root of each side:
t = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-1.414213562, 1.414213562, -3, 3}